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I have two predictors (X1 and X2) with large Beta's and large predictor-independent variable correlations (say it is like rs). In addition, I have another variable (X3; Beta=0.17; rs=0.18) which was not statistically significant in predicting the scores in the dependent variable. Last, I have an X4 with zero Beta and zero rs.

In interpreting this, should I only mention X1 and X2 are practically important predictors, while X3 predicts the scores at a lesser extent. Or should I just skip X3.

Thanks

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All predictors in a model are important, though they may differ in strength of prediction. Beta coefficients (or partial correlation coefficients) tell you of that strength. You should report all betas in your model whatever their size, because if you drop a predictor from the model, even the one with small beta, other betas can change sometimes dramatically.

The notion of importance is tied with the question of variable selection to a model. It has been a debate over what is the measure(s) of importance. Classical stepwise regressional selection procedures imply that it is part or semi-partial correlation. However, stepwise selection has been criticized recently. What is the IV "important" enough to be included in the model remains an open question.

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  • $\begingroup$ So regardless whether they were statistically significant or not, they all predict the scores in the DV. What if the beta is small but rs is large? $\endgroup$ – JonBonJovi Feb 7 '12 at 6:44
  • $\begingroup$ Beta is small but r is large means that the predictor correlates with other predictor(s) which is stronger. $\endgroup$ – ttnphns Feb 7 '12 at 6:57

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